Thermal Diffusion Flowmetry (TDF) (also called Heat Clearance Method or Thermal Clearance Method) is a longstanding technique for measuring blood flow or blood perfusion in living tissues. Typically, temperature transients and/or gradients are induced in a volume of interest and the temporal and/or spatial temperature variations which follow are measured and used for calculation of the flow. In this work a new method for implementing TDF is studied theoretically and experimentally. The heat deposition which is required for TDF is implemented photothermally (PT) and the measurement of the induced temperature variations is done by photoacoustic (PA) thermometry. Both excitation light beams (the PT and the PA) are produced by directly modulated 830 nm laser diodes and are conveniently delivered to the volume under test by the same optical fiber. The method was tested experimentally using a blood-filled phantom vessel and the results were compared with a theoretical prediction based on the heat and the photoacoustic equations. The fitting of a simplified lumped thermal model to the experimental data yielded estimated values of the blood velocity at different flow rates. By combining additional optical sources at different wavelengths it will be possible to utilize the method for non-invasive simultaneous measurement of blood flow and oxygen saturation using a single fiber probe.